Decomposition Algorithm for the Linear Three-Index Transportation Problem

The method of sequential modification of an objective function, which was earlier used for the classical transportation problem, is extended to the case of three indices. In the iterative process, the problem with three constraints and one binding variable is solved. Then, three independent problems with one constraint in which the coefficients for the binding variable are changed are considered. Using the suggested algorithm, a sequence of pseudosolutions with a monotonic growth of the objective function that converges to the optimum is constructed. The degeneracies are analyzed.